Lesson 1

Discover

 

The following puzzle is based on Henry Perigal’s 1830 proof of the Pythagorean theorem. Henry Perigal was so proud of this accomplishment that he had his theorem proof engraved on his tombstone!

 

Try This 1

 

You can try duplicating Perigal's proof by using either the multimedia or print option. After completing one of the options, answer questions 1 and 2.

 

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Multimedia Option

 

Click on the Pythagorean Puzzle multimedia piece and follow the instructions to solve the puzzle.

 

 

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Print Option

 

Print two copies of the Pythagorean Puzzle Template.

 

In the diagram there is a yellow right triangle. A square is drawn on each side of this triangle. The red lines divide the green square into four identical quadrilaterals.

 

From one copy of this diagram, carefully cut out the blue square and the green square. Then cut along the red lines of the green square. You should now have five puzzle pieces to work with.

 

Look at the part of the diagram that you did not cut. Fit the five puzzle pieces in the white square drawn on the hypotenuse of the yellow right triangle.

 

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Now answer these questions.

1. Were you able to fill in the white square using pieces of the smaller squares? Sketch the solution to your puzzle.
   
   
2. Explain how this puzzle illustrates the Pythagorean theorem.

Share 1

 

Share your solution to the puzzle with a partner or with a group of students.

 

How do your explanations about how the puzzle relates to the Pythagorean theorem compare to the other students' explanations?

 

Refer to the Share Rubric. The rubric will help you understand what your teacher expects of you.

 

Save a summary of your discussions and your solution to the Try This 1 questions in your course folder.